Analysis of flux-relaxed electron heat waves

Abstract

It has long been known that a classical description of electron heat conduction results in energy transport speeds which are unphysically large and that the results of model calculations using the classical description are inconsistent with the results of many laser fusion experiments. Some insight into the proper corrective measures is obtained if the plasma kinetic equations are solved via the ‘‘13 moment’’ approximation of Grad, rather than the more usual but incomplete Chapman–Enskog method. The Grad method naturally incorporates time variation of the electron distribution function and leads to a ‘‘flux-relaxation’’ equation for the heat flux, resulting in a hyperbolic temperature equation in which heat flow is restricted to speeds less than a characteristic electron thermal velocity. This paper contains some new insight into the subject of flux relaxation in the form of similarity solutions for the heat flow, as well as numerical solutions for boundary conditions appropriate to laser fusion modeling. Included in the treatment is the effect of hydrodynamics on the flux-relaxed heat flow. The results are that although flux relaxation naturally incorporates classical flux-limiting it does not play a role in the observed ‘‘anomalous’’ flux inhibition.